Question

For a body moving along a straight line, the following v-t graph is obtained.

According to the graph, the displacement during

• A. Uniform acceleration is less than that during uniform motion.
• B. Uniform acceleration is greater than that during uniform motion.
• C. Uniform acceleration is equal to that during uniform motion.
• D. Uniform motion is zero.

Answer 1

The Correct Option is B

1. Understanding the Graph:

The first part of the graph has a positive slope, indicating increasing velocity. This corresponds to a body undergoing uniform acceleration (since the velocity is changing at a constant rate).

The second part of the graph is horizontal, indicating that the velocity is constant. This corresponds to uniform motion (no acceleration).

2. Key Concepts:

1. Uniform Acceleration: - Occurs when the velocity changes at a constant rate. - In a v-t graph, uniform acceleration is represented by a straight line with a non-zero slope (positive or negative). - The area under this line gives the displacement during that time interval.

2. Uniform Motion: - Occurs when the velocity is constant. - In a v-t graph, uniform motion is represented by a horizontal line (slope = 0). - The area under the line gives the displacement over time, but since the velocity is constant, the displacement is directly proportional to time.

3. Displacement During Uniform Acceleration and Uniform Motion:

- Displacement during Uniform Acceleration (first part of the graph): - The displacement during uniform acceleration can be calculated by finding the area under the curve. - The area under a straight line with a positive slope (velocity vs. time) gives the displacement. - The formula for displacement when the acceleration is uniform is: $$ \text{Displacement} = \frac{1}{2} \times (\text{Initial Velocity} + \text{Final Velocity}) \times \text{Time}. $$ - This results in a triangular area under the line, which represents the displacement during this period.

- Displacement during Uniform Motion (second part of the graph): - During uniform motion, the velocity is constant. - The displacement is simply the area of the rectangle formed by the horizontal line and the time axis. - The formula for displacement during uniform motion is: $$ \text{Displacement} = \text{Velocity} \times \text{Time}. $$

4. Final Answer

Therefore, the displacement during uniform acceleration is greater than that during uniform motion.

Answer 2

Correct Answer: (B)

Explanation:

• Uniform Acceleration: - This corresponds to the part of the graph where the velocity is increasing linearly with time (the sloping line). - The slope of this line represents the magnitude of acceleration. - Since the velocity is changing over time, the body is experiencing non-zero acceleration during this phase.
• Uniform Motion: - This corresponds to the part of the graph where the velocity is constant (the horizontal line). - During uniform motion, the acceleration is zero because there is no change in velocity over time.

Since uniform motion has zero acceleration and the other part has non-zero acceleration, the acceleration during uniform motion is less.